The things Doreen Giuliano did to catch this guy’s eye: At 46, a wife and mother of three, she suddenly went tanning, hit the gym, went blond, bought short skirts and tight tops. She lived with her family in a three-story Victorian home on Prospect Park South, but she rented an apartment around the corner from his house — a basement apartment, at that. She spent at least seven months watching him from her car, or standing on a corner across the street from his place at 17th Avenue and 79th Street, following him on foot and figuring out his routine until, one day, she put on a pair of hot pants and got on her bicycle and rode by him about “100 times” and then, finally, she made contact.

His name was Jason Allo. He was 31, with a thick build and a bald head. It was actually Jason’s friend who had finally whistled at Doreen on that summer day in 2007, but Doreen had no interest in him whatsoever. It was always about Jason. Jason was the long game.

Jason, she was sure, was the reason her son John was in jail.

On Sept. 27, 2005, John Giuca was convicted of murdering Mark Fisher, a 19-year-old football star from New Jersey. According to prosecutors, Fisher encountered Giuca and his friends — who called themselves the “Ghetto Mafia” — while bar-hopping on the Upper East Side in October 2003.

Fisher took up an invitation to continue the party at the house on Prospect Park South, where Giuca still lived with his mother. (Doreen divorced John’s father when her son was 2.) The next morning, Fisher’s body was found a few blocks from Giuca’s home. He had been shot five times in the face and chest and wrapped in a blanket that Doreen would later identify as hers.

It was a sensational case that became known as the “grid kid” slaying, and in 2005, Giuca and his accomplice, Antonio Russo, were sentenced of 25 years to life.

In 2010, based on new evidence uncovered by his mother in her extraordinary sting operation — which involved months spent wooing Jason Allo, who was Juror No. 8 in her son’s trial — Giuca filed an appeal. He lost, but his attorney has filed an appeal in federal court, with the ruling expected within the next few weeks.

Even now Doreen is astonished that her son was found guilty. Two witnesses — one of whom was John’s girlfriend at the time of the murder — testified that John confessed to giving Russo the gun and telling him to show Fisher “what’s up.” The prosecution’s theory was that the murder was prompted by Fisher having leaned against a table in Giuca’s home.

One month later, Doreen says, she hatched her plan: She would go deep undercover, targeting one juror in particular, and prove that her son had been railroaded.

‘My first approach was to go to him as Doreen Giuliano,” she says. “Then I said, ‘No.’ He’s not gonna come two feet near me.”

Though Doreen has said before that she tried (and failed) to befriend two other jurors before Allo, today she insists that he was the only one. It’s unclear how she would have learned their names and addresses: Jurors filled out no forms, and attorneys for both sides had no information, either. She says she learned where Allo lived by asking around. “His barber ratted him out,” she says.

She concocted an alter ego: Dee Quinn. (Quinn is her maiden name.) “Dee” was a business-management consultant from California, and she had the business cards ($20 from Staples) to prove it, with her alternate cell number and e-mail address.

She bought a caller-ID spoof card ($10, got the idea from a Diane Lane movie) and would phone Allo pretending to be in LA and or in traffic in Brooklyn, all while sitting in her living room in Prospect Park South.

“I thought it was clever,” says Doreen.

Dee, however, was the opposite — perpetually at loose ends, the kind of woman who needed a man to take care of everything. It’s not difficult, however, to see how she pulled it off. Doreen has mastered a child-like affect — she speaks in a baby voice, tears up easily and does not relent till she gets her way.

So, on that first day in October 2007, when Jason’s friend Richie finally whistled her way, Doreen doubled back. “I made this elaborate plan to say, ‘I’m lost, do you know where the grocery store is, the coffee store is? You wanna hang out? Drink?’ ” At first, Doreen lasered in on Richie, keeping her back to Allo — a bit of reverse psychology. It worked.

“Then [Allo] says to me, and I’ll never forget this, ‘If you ever need any ganja, you can come to me.’ ”

And the sting was under way. Doreen, as Dee, started hanging out with Allo — mainly, she says, drinking wine and smoking pot in her basement apartment, eating the takeout food she pretended she had cooked, talking about everything and nothing while the recording devices she’d stashed in her handbag picked up their boring, innocuous chit-chat.

Impatient, Doreen came up with another angle: Dee was now working as a legal advocate for the wrongfully imprisoned. Maybe this would get Allo talking about the trial.

“I ended up finding out so much more than I anticipated,” she says.

But it would take months, and often, Doreen wouldn’t make it back home till dawn, reeking of smoke and booze. She and her second husband, Frank, had vicious fights, and Doreen would retire to bed — some nights to pass out, some nights with her law books — while Frank slept on the sofa.

“Even when I was home, I wasn’t home,” she says.

Frank was the only other person in Doreen’s life, she says, who knew about the sting. The only thing that kept him around was Doreen’s promise to never have sex with Allo.

That was a lie.

“Look,” she says. “Husbands are always second when you have kids. So when you say you’d do anything for your kid, you mean it. If I’m gonna lose Frank over my son, so be it. You could always get another husband. And would I lie if I did [sleep with Allo]? Yeah, most likely yes, I would lie. I would!”

(Jason Allo has said that the relationship was romantic; Doreen and her husband are still married.)

Doreen was fueled by outrage, what she saw as a gross miscarriage of justice.

Her son, she says, was tried and convicted before he ever went to trial, the press just eating up what the prosecution was feeding them. Her boy a gang member, the leader of the Ghetto Mafia, ordering the execution of Mark Fisher for kicks?

“The Ghetto Mafia did not exist,” Doreen says. “It did not exist.”

It’s true, she says, that John and his friends “called themselves that name” — but only out of camaraderie, she insists. “He didn’t judge a kid because you had money or you didn’t have money or you had a car or you didn’t — that’s why they called themselves the Ghetto Mafia.”

The night Mark Fisher was murdered, Doreen and her husband were down at their condo in Florida. She says she got a call from John — she doesn’t remember the day or time — telling her she needed to fly home immediately. Doreen says she never asked John what was wrong, and he never told her.

By the time she and Frank pulled up to their home, the cops had cordoned off the house and the press was all over and John wasn’t home, but that didn’t strike her as odd.

One of the detectives at the scene suggested that Doreen call her son. “I said, ‘John — there’s detectives and the press, what happened? What happened?’ And he said . . . he didn’t tell me. He says, ‘I’m going to the police station.’ ”

When the cops told Doreen that a young man had been murdered, quite possibly outside her home, she remembers thinking to herself: “Why are you telling me about this kid?”

After a 12-hour interrogation, Doreen says, John was released. Then, she says, the police began harassing her son, re-investigating an earlier incident when, at 17, John had been caught by cops lighting off fireworks.

Now, in the wake of Fisher’s murder, there were witnesses testifying to gunplay. John was arrested and held in jail leading up to and throughout the trial.

Finally, one night around New Year’s 2008, while drinking and smoking in Doreen’s apartment, Jason Allo said something he shouldn’t have: “Technically, by law, I shouldn’t have even been on that jury,” he said.

The recording devices, as always, were on. Allo also said that he had recognized some of the witnesses in her son’s trial from the neighborhood, and he thought it was wrong not to admit that and recuse himself.

Doreen was elated. She got him, she knew it. Her son’s trial had been tainted. There was no way John couldn’t get a new trial, and surely, an acquittal.

She had John’s attorney file the motion to appeal. The ruling came down in October 2010.

“[T]he defendant’s motion reveals extraordinary misconduct,” it reads, “not by a juror, but by the woman who generated the motion — the defendant’s mother.”

The ruling also found that the tapes Doreen had submitted were “selectively recorded” and that there was no way to tell whether they had been manipulated.

As for Doreen’s key charge — that Allo should never have been on that jury — she was done in by her own handiwork.

On the tapes, Allo also says that when the witness list was read to him, he “didn’t know any of the names.”

Further, the US Supreme Court had “long ago” ruled that jurors on high-profile cases could not be expected to have no knowledge going in; that Jason Allo eventually recognized some of these witnesses as people he’d known 10 or 12 years prior meant nothing.

But this is not the story Doreen tells. She insists Allo held a grudge against her son because Allo’s brother wasn’t cool enough to hang with John and his friends back in the day.

She also says that Allo — who was caught on tape saying “I hate Jews” — was convinced that John Giuca was, in fact, Jewish. And so he voted to convict.

And here is the crux of Doreen’s conundrum: Her undertaking necessitated such grand deceit that any inconsistencies in her story work against her.

From her point of view, a grave injustice has been done to her son, and, by extension, to her. All of her manipulations are justified, she says, because she was in search of the truth, which she believes she found.

Doreen refuses to give up. Aside from filing this new motion, she has written to Gov. Cuomo, requesting that a new trial be held outside of Brooklyn, or that he appoint a special prosecutor. She would also like just about everyone who worked on the prosecution’s side in the first trial removed.